Laser manipulation of trapped radial 4′-n-pentyl-4-cyanobiphenyl (5CB) nematic liquid-crystal droplets induced by molecular reordering is presented. We show experimentally that optical tweezers having linear, elliptical, or circular polarization can break the radial symmetry of the initial molecular organization inside a radial nematic droplet. Static distorted or twisted deformation modes and steady or unsteady nonlinear rotational dynamics are observed. Statics results are analyzed in terms of light-induced radial or left-right symmetry breaking effects associated with optical reorientation. The dynamical observations are compared with simulations from a slab analog model, for which orientational processes driven by optical nonlinearities can be accurately described. This study confirms that light-induced bulk reordering is an essential ingredient towards the understanding of the behavior of radial nematic liquid-crystal droplets in laser tweezers, as suggested by previous studies.